Examples of Scatterplots and Their Correlation Coefficients (Pearson’s)

Here are some scatterplots, with Pearson’s correlation coefficients and interpretations. Look them over and get a feel for what the coefficient tells you.

Some see no association in this scatterplot at all, your author included. Some say there’s a weak positive association, but if you remove the unusual point in the upper-right corner, that impression seems to disappear. Some say there’s a weak negative association, but that impression is seriously strengthened by the removal of the unusual point in the upper-right corner. If there really is a pattern in the data, its existence should not depend so heavily on a single point! (If you're curious, ).

There’s a fairly strong, positive association here, but it’s definitely not linear! So you shouldn’t use with these data, at all. It’ll be biased.

There seems to be a positive association here, but it’s too weak to
determine visually whether it’s linear. However, there are those who would be willing to
give it the benefit of the doubt. For their sake, we calculate
to
be 0.726. Note that this moderately high value does __not__ (by itself)
imply that there is a *linear* association.

There is a clear negative association, but it may not be strictly linear. There seems to be some curvature to it. The use of here is a bit risky, but not terribly so, since the data are only slightly curved. It turns out that is --0.916.

This scatterplot is for the same data as the previous one, but with the axes interchanged. Notice that the negativity of the association is still evident. So—as far as the strength and direction of the association are concerned—it doesn’t matter which variable goes on which axis. This is confirmed by the fact that is --0.916, just as in the previous example.

**SPSS instructions for calculating Pearson’s correlation
coefficient:** Click here.

**Related topics:**

Testing claims about Pearson’s correlation coefficient

Exploratory data analysis

**Statistics reference page:**
Click here.

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